I have often heard that because a fully homomorphic encryption scheme allows for both additions and multiplications on encrypted data, most other operations can be simulated. I don't understand how ...

In the article (https://eprint.iacr.org/2009/571.pdf, pag 8) of Smart and Vercauteren, it is mentioned that the recovery of the private key is an instance of the small principal ideal problem. But I ...

Consider I have two polynomials $f_1$ and $f_2$ of the same degree. I want to secure them (using any kind of encryption except FHE) and outsource them to an untrusted server. I want him to compute the ...

I want to implement file storage in cloud using homomorphic encryption. I want to use paillier encryption. Can you suggest the drawback of RSA to store and retrieving the files. Then only i can use ...

I would like to take some additively homomorphic cryptosystem - don't care much which one for now - and encrypt a series of numbers with it. I would then like to (in public) take these numbers, add ...

I am not a hardcore cryptographer so this might be a really stupid question. I am looking through some papers in homomorphic encryption and discovered they describe computation as "circuits", why do ...

Alice has a value $a$ and she signs it using her secret key $d_1$ as: $s_1 = (r_1 * g^a)^{d_1} \bmod p$, and Bob has a value $b$ and he signs it using his secret key $d_2$ as: $s_2 = (r_2 * g^b)^{d_2} ...

I'm imagining this for use in the scenario of cloud-stored client-encrypted email, where, when seeking to do a string search across messages, you don't want to have to download every stored message in ...

I have a somewhat special question. In our software we use a existing dongle which got cracked by our customers. The protection offered by the dongle isn't very sophisticated. For the moment I can't ...

Fully homomorphic encryption schemes allow one to evaluate any arbitrary computation over encrypted data. Intuitively this seems to be too weak, irrespective of how we achieve this.
An adversary who ...

While dabbling in privacy-preserving protocols (mainly using Semi-Homomorphic Encryption) and coming up with miscellaneous ideas for comparison tests or other similar primitives, based on obfuscation ...

Is it possible to modify a homomorphic encryption scheme so that it can be CCA2 secure?
From the definition of a homomorphic scheme, it seems that it is malleable, which would result in lack of CCA2 ...

Paillier cryptosystem is a probabilistic asymmetric algorithm for public key cryptography. Doesn't homomorphic encryption schemes have regular effects on the plaintext, and does that mean Pailliers ...

I have three quick questions concerning the reduction of the scheme to the approximate gcd problem:
What exactly do the authors mean by $q_p(z_1')$ being the odd part of the gcd? (last line of step ...